Impurity state in the vortex core of d-wave superconductors: Anderson impurity model versus unitary impurity model

Using an extended Anderson/Kondo impurity model to describe the magnetic moments around an impurity doped in high-$T_{\text{c}}$ d-wave cuprates and in the framework of the slave-boson meanfield approach, we study numerically the impurity state in the vortex core by exact diagonalization of the well-established Bogoliubov-de Gennes equations. The low-energy impurity state is found to be good agreement with scanning tunnelingmicroscopy observation. After pinning a vortex on the impurity site, we compare the unitary impurity model with the extended Anderson impurity model by examining the effect of the magnetic field on the impurity state. We find that the impurity resonance in the unitary impurity model is strongly suppressed by the vortex; while it is insensitive to the field in the extended Anderson impurity model.